laplace_band_error.cc
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#include "rheolef.h"
using namespace std;
using namespace rheolef;
#include "torus.icc"
int main (int argc, char**argv) {
environment rheolef (argc, argv);
Float tol = (argc > 1) ? atof(argv[1]) : 1e-7;
bool do_dump = (argc > 2) ? true : false;
field phi_h;
din >> catchmark("phi") >> phi_h;
const space& Xh = phi_h.get_space();
band gamma_h (phi_h);
space Bh (gamma_h.band(), "P1");
field uh(Bh);
din >> catchmark("u") >> uh;
trial u (Bh); test v (Bh);
form m = integrate (gamma_h, u*v);
form a = integrate (gamma_h, dot(grad_s(u),grad_s(v)));
size_t d = Bh.get_geo().dimension();
field pi_h_u = interpolate(Bh, u_exact(d));
field eh = pi_h_u - uh;
field phi_h_band = phi_h [gamma_h.band()];
Float c1 = m(eh,phi_h_band)/m(phi_h_band,phi_h_band);
field one (Bh, 1);
Float meas_gamma = m(one,one);
Float c2 = m(one,eh)/meas_gamma;
eh = eh - c1*phi_h_band - c2*one;
Float err_l2 = sqrt(m(eh,eh));
Float err_h1 = sqrt(a(eh,eh));
derr << "err_l2 = " << err_l2 << endl
<< "err_h1 = " << err_h1 << endl;
if (do_dump) {
dout << catchmark ("u") << uh
<< catchmark ("ue") << pi_h_u
<< catchmark ("eh") << eh;
}
return (err_l2 < tol && err_h1 < tol) ? 0 : 1;
}
Float
see the Float page for the full documentation
band
see the band page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef::std
Definition: vec_expr_v2.h:402
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
eh
field_basic< T, M > eh
Definition: form_field_expr.h:58
main
int main(int argc, char **argv)
Definition: laplace_band_error.cc:25
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
mkgeo_ball.a
int a
Definition: mkgeo_ball.sh:151
mkgeo_contraction.c2
c2
Definition: mkgeo_contraction.sh:199
mkgeo_sector.m
m
Definition: mkgeo_sector.sh:118
rheolef::details::dot
rheolef::details::is_vec dot
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::grad_s
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_s(const Expr &expr)
grad_s(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:929
rheolef::din
idiststream din(cin)
see the diststream page for the full documentation
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
rheolef.h
rheolef - reference manual
a
Definition: diffusion_isotropic.h:25
u
Definition: leveque.h:25
u_exact
g u_exact
Definition: taylor_exact.h:26
torus.icc
The torus benchmark – level set, right-hand-side and exact solution.
u
Float u(const point &x)
Definition: transmission_error.cc:26